Definition:Special Linear Group

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Let $R$ be a commutative ring with unity whose zero is $0$ and unity is $1$.

The special linear group of order $n$ on $R$ is the set of square matrices of order $n$ whose determinant is $1$.

It is a group under (conventional) matrix multiplication.

It is denoted $\SL {n, R}$, or $\SL n$ if the ring is implicit.

The ring itself is usually a standard number field, but can be any commutative ring with unity.

Also denoted as

Some authors prefer $\map {\mathrm {SL}_n } R$ and $\operatorname{SL}_n$ for the special linear group over $\SL {n, R}$.

Also see

  • Results about the special linear group can be found here.